Preheat the oven to 350°F.

In a large bowl, cream together ½ cup + 2 tablespoons of butter and 1 ½ cups of granulated sugar.

Add 3 eggs and 1 ½ tablespoons of vanilla bean paste, mixing until combined.

Mix in 1 cup of buttermilk until well blended.

In a separate bowl, sift together 2 ¼ cups of cake flour, ½ teaspoon of salt, 1 ½ teaspoons of baking powder, and ¼ teaspoon of baking soda.

Gradually add the dry ingredients to the wet ingredients, mixing until everything is combined.

Divide the batter evenly between three greased 6-inch cake pans.

Bake the cakes for 35-38 minutes, or until a toothpick comes out clean from the centers.

Let the cakes cool in their pans for 5 minutes, then transfer them to a cooling rack to cool completely.

Add 3 cups of thinly sliced peaches to a bowl.

Sprinkle ¼ cup + 2 tablespoons of granulated sugar over the peaches.

Gently stir to coat the peaches with sugar. Cover and let sit for about 30 minutes to dissolve the sugar and create peach syrup.

In a large bowl, whip 1 ½ cups of heavy whipping cream with an electric mixer on high until stiff peaks form.

Sift in ¾ cup of powdered sugar and mix until just combined.

Add 1 ½ teaspoons of vanilla bean paste and mix until well blended.

Trim the domed tops off each cake layer with a sharp knife to ensure they stack evenly.

Place the first cake layer on a serving plate and pour 2-3 tablespoons of peach syrup over it.

Arrange a layer of sliced peaches on top of the cake layer.

Spread about ⅓ of the whipped cream over the peaches.

Add another layer of peaches over the whipped cream.

Place the second cake layer on top and repeat the steps.

Add the third cake layer and top with the remaining whipped cream and sliced peaches.

Drizzle the remaining peach syrup over the cake and serve!